Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 60
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^62 - 357340567835956274473203762382806304174/92763774066594766347405217572025637*t^60 + 161002979902282630609580538919383654777195/92763774066594766347405217572025637*t^58 - 3113772412205937585530599846703134879190505/6397501659765156299821049487725906*t^56 + 1219867959413374497949480239766122422281507425/12795003319530312599642098975451812*t^54 - 355155179184479917889422283933450151580570675635/25590006639060625199284197950903624*t^52 + 79821696793052304036920434437329770564822437697935/51180013278121250398568395901807248*t^50 - 14201967322608545588548745221939235085309282314093625/102360026556242500797136791803614496*t^48 + 2035354416607044253859734432845752205370223962377856125/204720053112485001594273583607228992*t^46 - 237846615683522611669421015780778310326861498623878779375/409440106224970003188547167214457984*t^44 + 531580441605917295118939657925449257479523931463469029625/19043725870928837357606844986718976*t^42 - 42259314637969186470054254805061213268963559935158407738375/38087451741857674715213689973437952*t^40 + 2789174592529161384622375128676342479979666716629407165719375/76174903483715349430427379946875904*t^38 - 153118468824153763925379250584743491271240117872606387184338125/152349806967430698860854759893751808*t^36 + 6993313099199991030012683537574906956399552410029090562934090625/304699613934861397721709519787503616*t^34 - 265401436789108544358535449876479744529189401890579424476228914375/609399227869722795443419039575007232*t^32 + 8346841873712260150032492598877397035560101853028196718860408020625/1218798455739445590886838079150014464*t^30 - 216636120884031624109024589378765062703598207508239270961565180446875/2437596911478891181773676158300028928*t^28 + 4613517046755122537840984525040778402972211160792368378809865386509375/4875193822957782363547352316600057856*t^26 - 80012871334595463950134058882443916262098920435331916942827902351640625/9750387645915564727094704633200115712*t^24 + 1119322409113954563854393941218194660553384569480751845571405564984515625/19500775291831129454189409266400231424*t^22 - 12479139131915408977166316568445296043587844406493155610649646852680296875/39001550583662258908378818532800462848*t^20 + 109213137958167744221250770857417529818491232920573989763755826054585234375/78003101167324517816757637065600925696*t^18 - 736075632746253587215880171477134495555305025937842026656164005913145390625/156006202334649035633515274131201851392*t^16 + 3728232391027826118712852162339848855068450555715850607028022366446336328125/312012404669298071267030548262403702784*t^14 - 13744955290700758856900544620950251845791768573542667534021817920110082359375/624024809338596142534061096524807405568*t^12 + 35333213413537508551972934095573382873187265007786775563787225851517808921875/1248049618677192285068122193049614811136*t^10 - 59625644122929510265843373588916620998941093240454889235352292407157732578125/2496099237354384570136244386099229622272*t^8 + 60362599223296506278398523685210937209236744801265152531059208395119116953125/4992198474708769140272488772198459244544*t^6 - 31603217753619052909113969197330303492861584325211421979361788474007155859375/9984396949417538280544977544396918489088*t^4 + 6396880285244534307259533504599955478947729095470932323014452452176746796875/19968793898835076561089955088793836978176*t^2 - 208810226444040581699879779668833879333004558899986459682469264824260078125/39937587797670153122179910177587673956352
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   62 out of 62
Indefinite weights: 0 out of 62
Negative weights:   0 out of 62
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.5509630364305592931 + 2.0082161308503486776e-857j)  +/-  (1.6e-240, 1.6e-240j)
| (-9.2813570026015164814 + 1.1851047941497405458e-866j)  +/-  (1.62e-242, 1.62e-242j)
| (-9.8258139243505847286 + 2.194237678310439455e-872j)  +/-  (2.03e-243, 2.03e-243j)
| (5.4557693729668488291 - 2.0153376247094641155e-879j)  +/-  (1.52e-240, 1.52e-240j)
| (10.497992966086583086 - 2.1335835287759126162e-886j)  +/-  (7.83e-245, 7.83e-245j)
| (8.7998395663521354921 - 4.6791400810715645497e-882j)  +/-  (8.61e-242, 8.61e-242j)
| (-7.1745613938208539006 + 5.5199858446779561488e-889j)  +/-  (2.42e-240, 2.42e-240j)
| (-6.8116011091718651954 + 3.364105336117862173e-910j)  +/-  (3.24e-240, 3.24e-240j)
| (9.2813570026015164814 + 1.9375482159623395819e-931j)  +/-  (1.63e-242, 1.63e-242j)
| (2.1330069193880454391 - 9.221534738124096935e-937j)  +/-  (1.3e-246, 1.3e-246j)
| (3.2994175333639193464 - 5.5447784858720273353e-932j)  +/-  (1.32e-243, 1.32e-243j)
| (-3.8968332108098087961 - 5.6689568101056392645e-928j)  +/-  (2.03e-242, 2.03e-242j)
| (-2.7122512566942213661 + 2.4379715271396361698e-937j)  +/-  (4.87e-245, 4.87e-245j)
| (-1.8457259193828049156 + 5.2951965660853624102e-940j)  +/-  (1.47e-247, 1.47e-247j)
| (-5.7831098610111243627 - 5.3761898858689736809e-932j)  +/-  (2.21e-240, 2.21e-240j)
| (-7.943924377684709058 + 1.6314324186799383196e-941j)  +/-  (8.93e-241, 8.93e-241j)
| (-8.3579228800423447942 + 2.0241377789560791989e-944j)  +/-  (3.21e-241, 3.21e-241j)
| (-4.8185713490418010893 - 3.4571563925948960668e-945j)  +/-  (4.23e-241, 4.23e-241j)
| (4.8185713490418010893 - 8.2423198002782372086e-949j)  +/-  (4.45e-241, 4.45e-241j)
| (7.5509630364305592931 - 6.4957871775092769001e-948j)  +/-  (1.67e-240, 1.67e-240j)
| (9.8258139243505847286 + 3.2385849090582943995e-952j)  +/-  (1.84e-243, 1.84e-243j)
| (2.7122512566942213661 + 2.0426979983811295974e-954j)  +/-  (5.44e-245, 5.44e-245j)
| (6.8116011091718651954 + 4.0551553355893805608e-948j)  +/-  (3.33e-240, 3.33e-240j)
| (6.4597999111916048993 + 1.2239875194262669287e-948j)  +/-  (3.38e-240, 3.38e-240j)
| (-8.7998395663521354921 + 9.3291417568016696125e-951j)  +/-  (8.17e-242, 8.17e-242j)
| (7.943924377684709058 - 3.3670633731768113338e-954j)  +/-  (8.45e-241, 8.45e-241j)
| (-0.99059171364939086452 + 1.9319398003092757285e-963j)  +/-  (1.17e-250, 1.17e-250j)
| (-6.1174226944728185319 + 1.7150309906493069323e-951j)  +/-  (3.05e-240, 3.05e-240j)
| (5.7831098610111243627 + 1.7889630458918520981e-955j)  +/-  (2.31e-240, 2.31e-240j)
| (-4.2002445149213485804 - 1.9831535382495663061e-956j)  +/-  (6.46e-242, 6.46e-242j)
| (7.1745613938208539006 - 1.6390938884607541994e-956j)  +/-  (2.56e-240, 2.56e-240j)
| (2.4217693300870586954 + 8.5394542388458977779e-962j)  +/-  (8.52e-246, 8.52e-246j)
| (-1.2747253941898227699 - 1.0133133346640501218e-964j)  +/-  (1.44e-249, 1.44e-249j)
| (1.5597026876771864509 + 1.8032355613115565073e-964j)  +/-  (1.5e-248, 1.5e-248j)
| (6.1174226944728185319 + 2.389677954119822e-955j)  +/-  (3.03e-240, 3.03e-240j)
| (-2.1330069193880454391 - 2.1424107164175033524e-961j)  +/-  (1.33e-246, 1.33e-246j)
| (1.2747253941898227699 - 8.8825078559308502619e-965j)  +/-  (1.54e-249, 1.54e-249j)
| (-10.497992966086583086 - 7.2641562334403721515e-960j)  +/-  (8.3e-245, 8.3e-245j)
| (-5.4557693729668488291 - 5.6058041138109613308e-955j)  +/-  (1.62e-240, 1.62e-240j)
| (3.8968332108098087961 - 1.6300062192624122852e-961j)  +/-  (2.24e-242, 2.24e-242j)
| (-0.7071067811865475244 + 2.043148597626875661e-971j)  +/-  (7.31e-252, 7.31e-252j)
| (3.5966812989614749674 + 1.3798546987511132307e-962j)  +/-  (5.74e-243, 5.74e-243j)
| (3.0047083617004487939 - 9.6251063494537396675e-964j)  +/-  (2.69e-244, 2.69e-244j)
| (5.1345057122956205446 - 8.7175386792740844992e-961j)  +/-  (9.13e-241, 9.13e-241j)
| (-6.4597999111916048993 - 3.5014878137457754585e-960j)  +/-  (3.55e-240, 3.55e-240j)
| (-1.5597026876771864509 - 1.9498447835163744152e-976j)  +/-  (1.77e-248, 1.77e-248j)
| (0.7071067811865475244 + 1.2687455447612343507e-979j)  +/-  (8.26e-252, 8.26e-252j)
| (-3.5966812989614749674 + 1.6407765057420824588e-969j)  +/-  (5.85e-243, 5.85e-243j)
| (0.14133007140071462362 + 8.833682043369952233e-982j)  +/-  (3.3e-254, 3.3e-254j)
| (8.3579228800423447942 + 8.0217122790817739781e-969j)  +/-  (3.19e-241, 3.19e-241j)
| (-0.14133007140071462362 + 6.9243449751351423138e-983j)  +/-  (3.3e-254, 3.3e-254j)
| (-5.1345057122956205446 + 4.6635712710022015725e-969j)  +/-  (8.52e-241, 8.52e-241j)
| (-4.5073325310654691756 + 4.548046948290239693e-974j)  +/-  (1.72e-241, 1.72e-241j)
| (0.99059171364939086452 - 1.6478287858892257649e-987j)  +/-  (1.18e-250, 1.18e-250j)
| (1.8457259193828049156 - 3.2733538859730304929e-985j)  +/-  (1.46e-247, 1.46e-247j)
| (-3.2994175333639193464 + 1.3884419336428648323e-981j)  +/-  (1.3e-243, 1.3e-243j)
| (-0.42408134630509547155 + 7.0931325453083482114e-992j)  +/-  (4.42e-253, 4.42e-253j)
| (-3.0047083617004487939 + 1.6536598082278993314e-982j)  +/-  (2.94e-244, 2.94e-244j)
| (4.2002445149213485804 + 4.4313366019753661181e-979j)  +/-  (6.56e-242, 6.56e-242j)
| (0.42408134630509547155 + 1.1342617526984407039e-993j)  +/-  (4.42e-253, 4.42e-253j)
| (4.5073325310654691756 - 2.1529366409663652711e-989j)  +/-  (1.78e-241, 1.78e-241j)
| (-2.4217693300870586954 + 9.5279426582987995189e-994j)  +/-  (8.22e-246, 8.22e-246j)
-------------------------------------------------
The weights are:
| (3.7467111300538698028e-26 + 5.6066746070330354057e-882j)  +/-  (2e-53, 8.06e-173j)
| (1.1095024407449871845e-38 - 3.0138534623649739533e-889j)  +/-  (3.81e-59, 1.54e-178j)
| (3.9160163956469628935e-43 + 1.5443929835552200508e-891j)  +/-  (9.23e-61, 3.72e-180j)
| (2.1638929001372667871e-14 - 3.7712982853927822415e-878j)  +/-  (2.94e-48, 1.18e-167j)
| (6.1418351100394410502e-49 - 3.0842575346087267447e-895j)  +/-  (1.76e-65, 7.09e-185j)
| (6.0652982374294917739e-35 + 2.1654292019246924286e-888j)  +/-  (5.67e-61, 2.29e-180j)
| (9.1985558261512040492e-24 - 3.0237405120600797634e-881j)  +/-  (1.32e-54, 5.33e-174j)
| (1.4249569582526216826e-21 + 1.8588945132790645537e-880j)  +/-  (8.9e-54, 3.59e-173j)
| (1.1095024407449871845e-38 - 3.0982976999644277893e-890j)  +/-  (8.38e-63, 3.38e-182j)
| (0.0017174130283345664427 + 1.2792293464605310466e-872j)  +/-  (3.8e-30, 1.53e-149j)
| (3.1247978257274844444e-06 + 4.9948238043647465694e-874j)  +/-  (6.57e-40, 2.65e-159j)
| (4.3264109260309011064e-08 - 1.7767251336890961167e-874j)  +/-  (5.25e-44, 2.12e-163j)
| (0.00010499020556739799184 - 6.4004172553398969823e-873j)  +/-  (1.35e-36, 5.46e-156j)
| (0.0053605892784905105212 + 3.8192009853099626719e-872j)  +/-  (6.16e-29, 2.48e-148j)
| (5.5732656723623568856e-16 - 4.5345443833455026036e-878j)  +/-  (2.95e-52, 1.19e-171j)
| (8.9067593126201625678e-29 + 9.7341197159055941049e-884j)  +/-  (1.35e-58, 5.43e-178j)
| (1.1060772268878420383e-31 - 1.7574995914531283057e-885j)  +/-  (2.93e-60, 1.18e-179j)
| (1.4585612381557436457e-11 + 4.5196232851646204791e-876j)  +/-  (4.64e-50, 1.87e-169j)
| (1.4585612381557436457e-11 - 9.9837073164341820756e-877j)  +/-  (1.3e-53, 5.25e-173j)
| (3.7467111300538698028e-26 - 4.9822821888474762398e-884j)  +/-  (1.32e-63, 5.33e-183j)
| (3.9160163956469628935e-43 + 2.0218155287757776238e-892j)  +/-  (2.23e-69, 8.97e-189j)
| (0.00010499020556739799184 + 3.017551176865438601e-873j)  +/-  (1.32e-44, 5.32e-164j)
| (1.4249569582526216826e-21 - 9.5692928921013013135e-882j)  +/-  (6.54e-62, 2.64e-181j)
| (1.4752580064283563032e-19 + 9.7224161084797246016e-881j)  +/-  (4.31e-61, 1.74e-180j)
| (6.0652982374294917739e-35 + 2.8350685262053276534e-887j)  +/-  (7.66e-67, 3.09e-186j)
| (8.9067593126201625678e-29 + 2.4686418411831599235e-885j)  +/-  (1.52e-65, 6.14e-185j)
| (0.06001251271240071453 - 1.1010430496114590909e-871j)  +/-  (5.18e-43, 2.09e-162j)
| (1.0665578603141513986e-17 + 7.8952881341592581046e-879j)  +/-  (3.55e-60, 1.43e-179j)
| (5.5732656723623568856e-16 + 6.0119730474218368863e-879j)  +/-  (6.87e-60, 2.77e-179j)
| (3.7508390538973162597e-09 + 5.7656017879486424447e-875j)  +/-  (5.3e-56, 2.14e-175j)
| (9.1985558261512040492e-24 + 7.7290347176144339455e-883j)  +/-  (1.55e-63, 6.26e-183j)
| (0.00046352446085452492967 - 6.4866799159753178486e-873j)  +/-  (1.69e-49, 6.82e-169j)
| (0.031611544787336858411 + 8.3733068180412755466e-872j)  +/-  (4.09e-43, 1.65e-162j)
| (0.014141092083722518455 + 3.8699438044276935381e-872j)  +/-  (1.9e-45, 7.67e-165j)
| (1.0665578603141513986e-17 - 8.2805784637082589378e-880j)  +/-  (7.6e-61, 3.06e-180j)
| (0.0017174130283345664427 - 2.2864745099647411454e-872j)  +/-  (1.04e-49, 4.18e-169j)
| (0.031611544787336858411 - 5.9545341821824961084e-872j)  +/-  (2.28e-44, 9.2e-164j)
| (6.1418351100394410502e-49 - 1.8889400471437495817e-894j)  +/-  (4.5e-76, 1.81e-195j)
| (2.1638929001372667871e-14 + 2.3411806025144119908e-877j)  +/-  (6.94e-61, 2.8e-180j)
| (4.3264109260309011064e-08 + 5.6712961715303123901e-875j)  +/-  (1.94e-57, 7.83e-177j)
| (0.096918773533589336099 + 1.3388268356475118772e-871j)  +/-  (2.36e-46, 9.52e-166j)
| (4.0597817447199583362e-07 - 1.7672593252641249866e-874j)  +/-  (2.27e-56, 9.16e-176j)
| (1.9868090084695376211e-05 - 1.2848904384084676829e-873j)  +/-  (1.86e-54, 7.48e-174j)
| (6.3847479960004713618e-13 + 2.0666263721731310988e-877j)  +/-  (1.87e-60, 7.53e-180j)
| (1.4752580064283563032e-19 - 1.2483785808306329544e-879j)  +/-  (7.48e-65, 3.02e-184j)
| (0.014141092083722518455 - 5.8848660082946912488e-872j)  +/-  (1.3e-52, 5.25e-172j)
| (0.096918773533589336099 - 1.1095496424948739987e-871j)  +/-  (2.45e-51, 9.86e-171j)
| (4.0597817447199583362e-07 + 4.9821382780526792307e-874j)  +/-  (6.2e-60, 2.5e-179j)
| (0.15632854082688480973 - 1.5100769078655344105e-871j)  +/-  (2.91e-52, 1.17e-171j)
| (1.1060772268878420383e-31 - 8.9147134683911614906e-887j)  +/-  (1.04e-70, 4.19e-190j)
| (0.15632854082688480973 + 1.5676828050041511213e-871j)  +/-  (2.08e-52, 8.4e-172j)
| (6.3847479960004713618e-13 - 1.0848991206116476834e-876j)  +/-  (8.95e-63, 3.61e-182j)
| (2.6202800499316189752e-10 - 1.6974437080488487844e-875j)  +/-  (1.01e-61, 4.06e-181j)
| (0.06001251271240071453 + 8.4566000677463647692e-872j)  +/-  (4.92e-55, 1.98e-174j)
| (0.0053605892784905105212 - 2.3188430862527882062e-872j)  +/-  (1.55e-56, 6.23e-176j)
| (3.1247978257274844444e-06 - 1.2747303096564488215e-873j)  +/-  (1.66e-60, 6.68e-180j)
| (0.13331757292451125458 - 1.5060563528933882501e-871j)  +/-  (5.13e-56, 2.07e-175j)
| (1.9868090084695376211e-05 + 2.9833087279135856565e-873j)  +/-  (3.14e-60, 1.27e-179j)
| (3.7508390538973162597e-09 - 1.6439934886779865312e-875j)  +/-  (3.42e-63, 1.38e-182j)
| (0.13331757292451125458 + 1.3458841017824089227e-871j)  +/-  (2.55e-58, 1.02e-177j)
| (2.6202800499316189752e-10 + 4.2845122032701462308e-876j)  +/-  (8.15e-64, 3.3e-183j)
| (0.00046352446085452492967 + 1.261210366636806118e-872j)  +/-  (1.7e-60, 6.68e-180j)
